In [1]}, the upper half-plane pole-skipping point is \(\omega _\star =i\lambda _L,\ k_\star =\sqrt{6}i\pi T\) .
The dispersion relation of hydrodynamic sound modes \(\mathfrak {w}=v_B \mathfrak {k}\)  passes through the upper half-plane pole-skipping point \((\mathfrak {w}_\star ,\mathfrak {k}_\star )\)  for the case of Schwarzschild-\({\rm AdS_5}\)  spacetime, where \(\mathfrak {w}=\frac{\omega }{2\pi T}\)  and \(\mathfrak {k}=\frac{k}{2\pi T}\) . In [2]}, it was shown that the hydrodynamic poles (REF ) and (REF ) pass through the pole-skipping points in the lower half-plane for the case of Schwarzschild-AdS spacetime. Ref.[3]} shows that the dispersion relation which arises from the pole of the retarded Green's function associated to the transverse momentum density passes through the lower half-plane pole-skipping points in the backgound of anisotropic plasma. The pole-skipping points may be related to the hydrodynamic dispersion relation.
